Yes, you are confusing and conflating a lot of topics simply because you saw the word Ethereum or blockchain (or maybe "signature" if I'm reading this correctly). A lot of people do it. I've been in plenty of circumstances where people go on incoherent jumbles of words in response to the word blockchain.
Signing an address has nothing to do with linkability or transaction history, or even blockchains, as this is not a transaction and requires no funds. It requires having generated the private key, client side. Signing proves you control the private key, public key and address hash. A signature allows other people to verify that you in fact do have control of that address. When looking at the address on a blockchain, it can be empty, no funds, and simply relegated to being a unique identifier for the person that signed the address.
Okay, so let's assume this is confusing because it conflicts with something else you thought you experienced regarding blockchains. Well just erase all that from your mind, and read on:
Blockchains use a namespace of address hashes. Private keys to generate those address hashes are only generated client side by the user, and there is enough randomness and entropy for no other user to generate the same private key, public key and address hash. But within the namespace, all public keys and address hashes already exist. I think this is the fundamentally different paradigm than account numbers like at a bank. At banks, for example, accounts numbers are incremental. ie. When an account is created new row is added to the account database it has an ID that goes up by one, and all the attributes of the account did not exist until the point in time that the server was instructed to create the account. In blockchains using a designated cryptographic namespace, all accounts therefore already exist and access must be generated client side by the user. The namespace is extremely large, which allows for assurances that nobody generates the same private keys, public keys and address hash. The other countintuitive thing to understand is that these accounts don't exist "on" the blockchain until someone sends funds to them. An empty address means it has never been seen on the blockchain, as this record only occurs after a digital asset or message references them in a prior transaction. GUI's for browsing blockchains smooth this over by letting you look at empty addresses simply by nature of them complying with the namespace, but an address that has never previously received funds or any other message is not in the blockchain at all, yet. The reason this is important is because if you have the private key to that address, you can still convey that you have control of that address via signing and there is no prior link to any other address or funds. There is no linkability or privacy issue. Signing just lets you have a unique identifier.
Using all that, to go back to what I said earlier, cryptocurrency wallets just makes public and private key cryptography so prevalent that signing is also more prevalent and available. Whereas PGP and GPG Suites had 25 years to do so and have not been successful outside of much much much smaller niches, that have not seem to have grown at all and the user experience arguably has gotten worse.
What you mentioned about NFT art signatures is a different topic. Address signing is about offchain signatures. All transactions and onchain metadata are onchain signatures.